一类推广的IMBq方程解的爆破  

Blow-up of Solutions for a Class of Generalized IMBq Equations

作　　者：刘洋[1] 赵军生[2] 于涛[3] 

机构地区：[1]西北民族大学数学与计算机科学学院,甘肃兰州730124 [2]黑龙江大学数学科学学院,黑龙江哈尔滨150080 [3]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《河北大学学报（自然科学版）》2011年第3期240-243,共4页Journal of Hebei University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10871055)

摘　　要：对一类推广的IMBq方程的初边值问题进行了研究,在非线性项满足一定条件的情况下,采用特征函数法和凸性方法,证明了问题的光滑解只能在时间的一个有界区间中存在,并且在有限时间T内爆破,即解于有限时间T内在某种意义下趋于无穷大,从而说明了这类典型的非线性发展方程解的奇性.The initial boundary value problem of solutions for a class of generalized IMBq equations is studied. In the case of the nonlinear term satisfying some conditions, it is proved by using the eigenfunction method and convexity method that smooth solutions of the problem only exist in a bounded time interval and blow up in the finite time T, that is, the solutions tend to infinity in the finite time T in a sense. Consequently, the conclusion of this paper indicates the singularity of solutions for this typical nonlinear e- volution equations.

关 键 词：IMBq方程 初边值问题 特征函数法 凸性方法 爆破 

分 类 号：O175.26[理学—数学]